Problem: Simplify the following expression: $k = \dfrac{1}{7x} + \dfrac{1}{8x}$
In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7x$ and $8x$ $\lcm(7x, 8x) = 56x$ $ k = \dfrac{8}{8} \cdot \dfrac{1}{7x} + \dfrac{7}{7} \cdot \dfrac{1}{8x} $ $k = \dfrac{8}{56x} + \dfrac{7}{56x}$ $k = \dfrac{8 +7}{56x}$ $k = \dfrac{15}{56x}$